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The ordered field property and a finite algorithm for the Nash bargaining solution

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Abstract

This note proves that the two person Nash bargaining theory with polyhedral bargaining regions needs only an ordered field (which always includes the rational number field) as its scalar field. The existence of the Nash bargaining solution is the main part of this result and the axiomatic characterization can be proved in the standard way with slight modifications. We prove the existence by giving a finite algorithm to calculate the Nash solution for a polyhedral bargaining problem, whose speed is of orderBm(m-1) (m is the number of extreme points andB is determined by the extreme points).

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Authors and Affiliations

  1. Department of Economics, Virginia Polytechnic Institute and State University, 24060, Blacksburg, VA

    M. Kaneko

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  1. M. Kaneko
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Additional information

The author thanks Takashi Nagashima of Hitotsubashi University for valuable suggestions on this subject.

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Kaneko, M. The ordered field property and a finite algorithm for the Nash bargaining solution. Int J Game Theory 20, 227–236 (1992). https://doi.org/10.1007/BF01253777

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  • DOI: https://doi.org/10.1007/BF01253777

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